**Research Interests**:

Wavelet analysis, statistical signal and image processing, random
fields, and machine learning. In particular: wavelet/Riesz basis
construction and sparsity with applications to detection and
classification; Markov random fields; multiresolution analysis for
machine learning, support vector machine kernel construction for pattern
recognition; sampling theory; and (multi-)fractal dimension and Hurst
index estimation for texture and volatility models.
## Selected Research Activity

__Hyperparameter
search reduction for Paley-Weiner reproducing Mercer kernels (01/2005-12/2006)____ __

During the "Data and Information
Fusion, Defence Technology Centre" (DIF-DTC) Phase I project, we developed
adaptive hyper- and multi-spectral data fusion methods for target detection and
tracking and biometric identification in collaboration with the UK Ministry of Defence,
QinetiQ, and General Dynamics UK.

The work included the development of a
framework to reduce the choice of optimal support vector machine kernel
hyperparameters to a finite/small set. Previous methods relied upon sub-optimal
ad-hoc grid searches and cross validation. We achieved an a priori parameter
subset estimation by bringing together two differing philosophies of data
analysis, namely machine learning and applied harmonic analysis, and asserting
the weak condition that the decision function belongs to a Paley-Weiner space;
and using "sequency analysis" to estimate its support. This lead to
enhanced methods and state-of-the-art results for hyperspectral classification.
The work was subsequently extended to the sequence kernel case (to deal with
data of differing lengths) and applied to a speaker recognition problem.

__
Rotation invariant dual-tree wavelet detector and particle filtering
(12/2006-10/2009)
__

The Data and Information Fusion,
Defence Technology Centre Phase II project was carried out in collaboration with
the UK Ministry of Defence, QinetiQ, General Dynamics UK, Waterfall Solutions,
the University of Cambridge, Imperial College London, and University of
Bristol.

Our task in this project was to develop
the application of dual-tree complex wavelet polar matching and particle
filtering to shift and rotation invariant object detection. These methods were
used to detect and track objects of interest from aerial imagery in both
electro-optical and infra red spectrums. A notable feature was that the
algorithm adapted to the visibility of the target. In experiments, this allowed
the tracker to reacquire the target after prolonged periods of total occlusion.
The shift and scale tolerance of the polar matching detector was then enhanced
by exploiting the sesquilinear form of the polar matching operator and the
geometry of the feature vectors and corresponding Jacobians. Aside from
offering an observational model to trackers, such detectors can be used to
facilitate both keypoint matching and neighbourhood search detection.

__Wavelet
shrinkage for sonar imagery (10/2009-present)____ __

During 10/2009-10/2010, I was the
researcher co-investigator for a University Defence Research Centre project
co-funded by the EPSRC and Dstl. This work was continued into my appointment at
UCL via consultancy and a short contract.

In this project, dual-tree wavelets
were applied to the estimation of anisotropic fractal dimension. A wavelet
shrinkage method was then developed that improved the detection of mines in
sonar imagery by reducing the false positives caused by sand ripples. By
modelling the background as stochastic self-similar random field, principled
features were devised to construct a scale invariant likelihood model of ripples.
This was later extended by incorporating a Markov random field model to exploit
the observation that rippled and non-rippled locations are unlikely to appear
at isolated points. In this framework, the likelihood function is designed to
"soft-shrink" coefficients according to the energy ratio value; the
prior (Ising model) encodes spatial constraints into the shrinkage functions.
Markov Chain Monte Carlo methods provided an efficient, tractable way to
estimate the conditional distribution of the posterior marginal
ripple/non-ripple state in the dual-tree wavelet domain. Ripple suppression was
then realised by multiplying the dual-tree wavelet coefficients by the marginal
probabilities of the non-ripple states.

__Fused
Lasso and rotation invariant autoregressive models for texture classification
(2012-present)____ __

Inspired by discussions with Microsoft
India and the University of Waterloo, the problem of rotation invariant texture
classification was tackled by considering radially sampled autoregressive
random field models. Unfortunately, owing to the strong correlations present in
the neighbourhood covariate matrix, parameter estimation is complicated by the
dichotomy between ill-conditionedness and rotation invariance. Exploiting the
Fused Lasso framework, we proposed a compromise which incorporates two
regularisers. The 1-norm induces stability and performs variable selection
amongst strongly correlated radial samples; the total variation seminorm
encourages clustering and promotes model parsimony. Experiments on standard datasets
confirmed the potential utility and parallels were drawn within the texture
classification literature and beyond.

** **

__Sparse
regularisation for piecewise, minimal codomain cardinality, Riesz basis
construction (2012-present) __

Piecewise, low-order polynomial, Riesz
basis families were constructed such that they share the same coefficient
functionals of smoother, orthonormal bases in a localised indexing subset. It
was shown that a minimal cardinality basis codomain can be realised by inducing
sparsity, via 1-norm regularisation, in the distributional derivatives of the
basis functions and that the optimal construction can be found numerically by
constrained binary optmisation over a suitably large dictionary. Furthermore,
it was shown that a subset of these solutions are equivalent to a specific,
constrained analytical solution based on Sylvester-type Hadamard matrices. It
is anticipated that these constructions are well suited for approximate signal
processing and sparse representations. This work is currently under review in the
journal: Applied Computational Harmonic Analysis (impact factor 3.5).

** **

__Multiresolution
Markov random fields for mammogram imagery analysis (07/2012-present)____ __

From July 2012, we have been developing
a much needed multiresolution Bayesian approach to the problem of detecting
radial patterns of spicules, an early sign of breast cancer in mammograms. This
project involves collaboration with the Division of Medicine at UCL and UCL
Hospital. We are investigating the construction of multiscale, directional
regularity and phase congruence features, constrained by Markov-type priors. The
proposed Bayesian wavelet shrinkage approach will be a significant departure
from previous attempts and is designed to overcome the main shortcomings of
heuristic thresholding (erroneous discontinuities and limited solution search
space) found in present state-of-the-art spicule detection and orientation
estimation methods.

**Contact details and other info:**

Please see James Nelson's UCL webpage**Publications**

Please see James Nelson's personal UCL pages and Google Scholar